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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hilbert's lemma ： ウィキペディア英語版 Hilbert's lemma Hilbert's lemma was proposed at the end of the 19th century by mathematician David Hilbert. The lemma describes a property of the principal curvatures of surfaces. It may be used to prove Liebmann's theorem that a compact surface with constant Gaussian curvature must be a sphere.〔.〕 == Statement of the lemma == Given a manifold in three dimensions that is smooth and differentiable over a patch containing the point ''p'', where ''k'' and ''m'' are defined as the principal curvatures and ''K''(''x'') is the Gaussian curvature at a point ''x'', if ''k'' has a max at ''p'', ''m'' has a min at ''p'', and ''k'' is strictly greater than ''m'' at ''p'', then ''K''(''p'') is a non-positive real number.〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hilbert's lemma」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.